Yuav Ua Li Cas Xam Cov Quartiles, Deciles, thiab Percentiles hauv Cov Ntaub Ntawv Txheeb Cais
Hauv kev suav lej, peb feem ntau yuav tsum txiav txim siab qhov chaw ntawm tus nqi hauv cov ntaub ntawv teeb tsa. Tsuas yog xam qhov nruab nrab lossis nruab nrab tsis txaus, vim tias cov kev ntsuas no tsis piav qhia txog yuav ua li cas cov ntaub ntawv raug faib tawm thiab yuav ua li cas kev soj ntsuam piv rau lwm tus. Qhov no yog qhov uas quartiles, deciles, thiab percentiles tuaj rau hauv kev ua si. Peb qhov no yog cov kev ntsuas qhov chaw uas faib cov ntaub ntawv raug xaiv ua ntu sib npaug. Tsab xov xwm no tham txog cov lus txhais, cov kauj ruam dav dav, thiab yuav ua li cas xam quartiles, deciles, thiab percentiles rau ob qho tib si ib leeg thiab pawg ntaub ntawv teeb tsa.
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1. Lub Tswv Yim Tseem Ceeb: Cov Ntaub Ntawv Yuav Tsum Tau Txheeb Xyuas
Ua ntej xam cov quartiles, deciles, lossis percentiles, cov kauj ruam tseem ceeb tshaj plaws yog cais cov ntaub ntawv los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws. Thaum cov ntaub ntawv raug cais lawm, peb tuaj yeem txiav txim siab qhov chaw ntawm cov quartiles, deciles, lossis percentiles raws li lawv qhov chaw ntsuas.
Feem ntau:
- Cov Quartiles faib cov ntaub ntawv ua 4 ntu.
- Deciles faib cov ntaub ntawv ua 10 ntu.
- Cov feem pua faib cov ntaub ntawv ua 100 feem.
Hauv kev xyaum ua, cov quartiles, deciles, thiab percentiles feem ntau yog siv rau kev tshuaj xyuas cov qhab nia xeem, cov ntaub ntawv nyiaj tau los, kev ntsuas anthropometric (qhov siab/qhov hnyav), thiab kev ntsuam xyuas kev ua tau zoo.
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2. Yuav Ua Li Cas Xam Cov Quartiles (Q1, Q2, Q3)
A. Cov Quartiles Hauv Cov Ntaub Ntawv Ib Leeg (Tsis Muab Pawg)
Cov Quartiles muaj xws li:
- Q1: qis dua quartile (25% ntawm cov ntaub ntawv yog qis dua nws)
– Q2: nruab nrab (50%)
– Q3: sab saud quartile (75%)
Cov kauj ruam los xam cov ntaub ntawv ib quartiles:
1. Cais cov ntaub ntawv.
2. Xam qhov chaw quartile siv cov qauv qhia chaw:
– Txoj hauj lwm Q1 = \((n+1)/4\)
– Txoj hauj lwm Q2 = \(2(n+1)/4\) los yog \((n+1)/2\)
– Txoj hauj lwm Q3 = \(3(n+1)/4\)
Yog tias qhov chaw yog ib qho integer, siv tus nqi ntawm qhov chaw ntawd. Yog tias qhov chaw yog ib feem, siv interpolate (siv tus nqi ntawm ob qho chaw ze tshaj plaws).
Ib qho piv txwv ceev:
Cov ntaub ntawv raug cais: 4, 6, 7, 8, 10, 12, 13, 15 (n = 8)
Txoj hauj lwm Q1 = (8+1)/4 = 2,25 → yog nyob nruab nrab ntawm cov ntaub ntawv thib 2 thiab thib 3.
Yog li Q1 yog nyob nruab nrab ntawm 6 thiab 7. Kev sib tshuam:
Q1 = 6 + 0,25(7−6) = 6,25.
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B. Cov Quartiles hauv Cov Ntaub Ntawv Muab Pawg (Kev Faib Zaus)
Rau cov ntaub ntawv pawg (piv txwv li, cov chav kawm sib nrug), cov quartiles raug suav siv cov mis:
\[
Q_k = L + \left( \frac{\left(\frac{k}{4}n – F\right)}{f} \right) \times c
\]
Cov Ntaub Ntawv:
– \(Q_k\): kth quartile (k = 1,2,3)
- \(L\): ntug qis ntawm chav kawm quartile
– \(n\): tus naj npawb ntawm cov ntaub ntawv (tag nrho cov zaus)
- \(F\): zaus sib sau ua ke ua ntej chav kawm quartile
- \(f\): zaus hauv chav kawm quartile
– \(c\): qhov ntev ntawm chav kawm
Cov kauj ruam dav dav:
1. Tsim kom muaj zaus sib sau ua ke.
2. Txheeb xyuas qhov chaw ntawm lub quartile: \(k/4 \times n\).
3. Nrhiav chav kawm uas muaj txoj haujlwm ntawd.
4. Sau rau hauv tus qauv.
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3. Yuav Ua Li Cas Xam Deciles (D1 txog D9)
Deciles faib cov ntaub ntawv ua 10 ntu, yog li ntawd:
- \(D_1\) qhia txog qhov txwv qis tshaj 10% ntawm cov ntaub ntawv,
– \(D_5\) yog sib npaug rau qhov nruab nrab,
- \(D_9\) qhia txog qhov txwv ntawm cov ntaub ntawv 90%.
A. Deciles hauv Cov Ntaub Ntawv Ib Leeg
Tus qauv txoj haujlwm Decile:
\[
\text{Qhov Chaw } D_k = \frac{k(n+1)}{10}
\]
nrog \(k = 1,2,\dots,9\).
Thaum tau txais qhov chaw lawm, txoj kev siv tus nqi yog tib yam li rau quartile: yog tias nws yog tag nrho, coj nws ncaj qha, yog tias nws yog fractional, interpolate.
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B. Deciles hauv Cov Ntaub Ntawv Muab Pawg
Decile formula rau cov ntaub ntawv pawg:
\[
D_k = L + \left( \frac{\left(\frac{k}{10}n – F\right)}{f} \right) \times c
\]
Cov lus piav qhia zoo ib yam li lub quartile, tsuas yog tus divisor yog 10.
Kauj Ruam:
1. Xam \(k/10 \times n\).
2. Txheeb xyuas chav kawm decile raws li qhov zaus sib sau ua ke.
3. Hloov rau hauv tus qauv.
Cov lej kaum feem ntau siv rau hauv kev tshuaj xyuas kev lag luam, piv txwv li faib cov nyiaj tau los ntawm tib neeg ua 10 pawg (decile 1 yog cov neeg pluag tshaj plaws rau decile 10 yog cov neeg nplua nuj tshaj plaws).
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4. Yuav Ua Li Cas Xam Feem Pua (P1 txog P99)
Cov feem pua muaj cov ntsiab lus ntxaws ntxiv vim lawv faib cov ntaub ntawv ua 100 ntu. Tus nqi P25 = Q1, P50 = nruab nrab, thiab P75 = Q3. Qhov no txhais tau tias cov quartiles yog ib qho xwm txheej tshwj xeeb ntawm cov feem pua.
A. Feem pua ntawm Cov Ntaub Ntawv Ib Leeg
Cov qauv qhia txog feem pua:
\[
\text{Qhov Chaw } P_k = \frac{k(n+1)}{100}
\]
nrog \(k = 1,2,\dots,99\).
Cov txheej txheem yog tib yam: cais cov ntaub ntawv, xam qhov chaw, tom qab ntawd coj tus nqi lossis interpolate.
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B. Feem pua hauv Cov Ntaub Ntawv Muab Pawg
Cov qauv feem pua ntawm cov ntaub ntawv muab faib ua pawg:
\[
P_k = L + \left( \frac{\left(\frac{k}{100}n – F\right)}{f} \right) \times c
\]
Cov kauj ruam zoo ib yam li deciles / quartiles:
1. Txheeb xyuas qhov chaw \(k/100 \times n\).
2. Nrhiav qhov feem pua ntawm cov zaus sib sau ua ke.
3. Siv cov mis.
Feem ntau siv cov feem pua hauv kev ntsuam xyuas kev kawm thiab kev noj qab haus huv. Piv txwv li, tus menyuam qhov siab ntawm 80th percentile txhais tau tias tus menyuam siab dua 80% ntawm cov menyuam uas nws muaj hnub nyoog.
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5. Cov Lus Qhia Tseem Ceeb thiab Cov Yuam Kev Feem Ntau
1. Cov ntaub ntawv yuav tsum tau muab cais tawm (tshwj xeeb tshaj yog rau cov ntaub ntawv ib leeg). Yog tsis muaj kev cais tawm, cov quartiles/deciles/percentiles tsis muaj txiaj ntsig.
2. Nco ntsoov siv cov npoo ntawm cov ntaub ntawv uas tau muab faib ua pawg (tsis yog cov ciam teb ntawm cov chav kawm) yog tias koj siv cov tswv yim txuas ntxiv mus.
3. Qhov zaus sib sau ua ke yuav tsum yog qhov tseeb, vim tias chav kawm quartile/decile/percentile yog txiav txim siab los ntawm qhov zaus sib sau ua ke.
4. Ua tib zoo saib seb chav kawm ntev npaum li cas (c). Qhov ntev ntawm chav kawm yuav tsum tsis txhob yuam kev, vim nws cuam tshuam rau cov txiaj ntsig ntawm kev xam.
5. Kev sib xyaw ua ke yog qhov tseem ceeb thaum cov chaw tsis raug puag ncig. Muaj ntau tus tub ntxhais kawm tam sim ntawd puag ncig cov chaw, txawm tias qhov no tuaj yeem txo qhov tseeb.
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6. Xaus Lus
Cov quartiles, deciles, thiab percentiles yog cov cuab yeej tseem ceeb rau kev nkag siab txog kev faib tawm ntawm cov ntaub ntawv. Cov quartiles yog qhov tsim nyog rau kev sau cov ntsiab lus yooj yim (piv txwv li, hauv ib daim duab), deciles yog qhov muaj txiaj ntsig zoo rau kev sib sau ua pawg ntau ntxiv xws li kev tshuaj xyuas cov nyiaj tau los, thaum cov percentiles pab soj ntsuam qhov chaw ntawm tus neeg tshwj xeeb hauv cov pej xeem. Los ntawm kev nkag siab txog cov kauj ruam yooj yim - kev txiav txim cov ntaub ntawv, kev txiav txim siab qhov chaw, thiab siv cov qauv tsim nyog rau cov ntaub ntawv ib leeg lossis pawg - koj tuaj yeem xam cov quartiles, deciles, thiab percentiles nrog qhov tseeb thiab kev ntseeg siab ntau dua.
Yog tias koj xav tau, kuv tuaj yeem ntxiv ib qho piv txwv tiav ntawm cov ntaub ntawv teev ua pawg (lub sijhawm, zaus, zaus sib sau ua ke) thiab tom qab ntawd xam Q1, D7, thiab P85 kom ntxaws kom yooj yim rau kev xyaum.
